Basic properties
| Modulus: | \(2940\) | |
| Conductor: | \(980\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{980}(163,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2940.dl
\(\chi_{2940}(163,\cdot)\) \(\chi_{2940}(247,\cdot)\) \(\chi_{2940}(403,\cdot)\) \(\chi_{2940}(487,\cdot)\) \(\chi_{2940}(583,\cdot)\) \(\chi_{2940}(823,\cdot)\) \(\chi_{2940}(907,\cdot)\) \(\chi_{2940}(1003,\cdot)\) \(\chi_{2940}(1087,\cdot)\) \(\chi_{2940}(1327,\cdot)\) \(\chi_{2940}(1423,\cdot)\) \(\chi_{2940}(1507,\cdot)\) \(\chi_{2940}(1663,\cdot)\) \(\chi_{2940}(1747,\cdot)\) \(\chi_{2940}(1927,\cdot)\) \(\chi_{2940}(2083,\cdot)\) \(\chi_{2940}(2167,\cdot)\) \(\chi_{2940}(2263,\cdot)\) \(\chi_{2940}(2347,\cdot)\) \(\chi_{2940}(2503,\cdot)\) \(\chi_{2940}(2587,\cdot)\) \(\chi_{2940}(2683,\cdot)\) \(\chi_{2940}(2767,\cdot)\) \(\chi_{2940}(2923,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((1471,1961,1177,1081)\) → \((-1,1,-i,e\left(\frac{10}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 2940 }(163, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{55}{84}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{71}{84}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{17}{28}\right)\) |